Is the word ciclo the same in Brazilian and European Portuguese?

Yes

The meaning, spelling, and grammar of "ciclo" are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the unstressed vowels are generally more open and clearly articulated. In Continental Portuguese, vowels (especially unstressed ones) are much more reduced and "closed," which can make the word sound more clipped or muffled to a Brazilian speaker.

Brazilian Portuguese

1. O ciclo da água é essencial para a vida. (The water cycle is essential for life.)
2. Estou em um novo ciclo na minha carreira. (I am in a new cycle in my/an entered cycle in my career.)
3. Precisamos fechar esse ciclo de projetos. (We need to close this cycle of projects.)
4. O ciclo menstrual pode variar de mulher para mulher. (The menstrual cycle can vary from woman to woman.)
5. O preço dos alimentos segue um ciclo de alta e baixa. (Food prices follow a cycle of highs and lows.)

Continental Portuguese

1. O ciclo da água é fundamental para a vida. (The water cycle is fundamental to life.)
2. Estou a iniciar um novo ciclo na minha carreira. (I am starting a new cycle in my career.)
3. Temos de concluir este ciclo de projetos. (We have to conclude this cycle of projects.)
4. O ciclo menstrual pode variar de mulher para mulher. (The menstrual cycle can vary from woman to woman.)
5. O preço dos alimentos segue um ciclo de subida e descida. (Food prices follow a cycle of rising and falling.)